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Chapter Contents

• Functions and Graphs
• 1. Introduction to Functions
• 2a. Domain and Range of a Function
• 2b. Functions from Verbal Statements
• 3. Rectangular Coordinates
• 4. The Graph of a Function
• 5. Graphing Using a Computer Algebra System
• Plot your own graph
• 6. Graphs of Functions Defined by Tables of Data
• 7. Continuous and Discontinuous Functions
• 8. Split Functions
• 9. Even and Odd Functions

• Comments, Questions?

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2b. Functions from Verbal Statements

Example 1:

The fixed cost for a company to operate a certain plant is $3,000 per day. It also costs $4 for each unit produced in the plant. Express the daily cost C of operating the plant as a function of the number n of units produced.

Answer

Example 2:

An architect designs a window such that it has the shape of a rectangle with a semicircle on top, as shown. (This kind of window is called a Norman window).

The architect wants the base of the window to be 10 cm less than the height of the rectangular part.

Express the perimeter p of the window as a function of the radius r of the circular part.

Answer

Exercises

Question 1

For F(t) = 3t - t² for t ≤ 2, find F(2) and F(3).

Answer

Question 2

A rocket burns up at the rate of 2 Mg/min after falling out of orbit into the atmosphere. If the rocket weighed 5,500 Mg before re-entry, express its weight w as a function of the time t, in minutes, of re-entry.

Answer